DOI: 10.13009/EUCASS2017-447 7TH EUROPEAN CONFERENCE FOR AERONAUTICS AND SPACE SCIENCES (EUCASS) Wing geometric parameter studies of a box wing aircraft configuration for subsonic flight Fábio Cruz Ribeiro*, Adson Agrico de Paula*, Dieter Scholz** and Roberto Gil Annes da Silva* *Instituto Tecnológico de Aeronáutica Address: Instituto Tecnológico de Aeronáutica, Departamento de Projeto de Aeronaves. São José dos Campos, SP,12228900, Brasil. ** Hamburg University of Applied Sciences Address: Aero – Aircraft Design and Systems Group, Berliner Tor 9, 20099Hamburg, Germany Abstract This work studies the characteristics of the aerodynamics design of a box wing aircraft (BWA) with the potential gain of aerodynamics efficiency. The first objective of this paper is to study how BWA planform geometric parameters affect the aerodynamics efficiency. This is carried out using literature data and vortex lattice program. The second objective is to compare aerodynamics efficiency between BWA and conventional mid-range market aircraft. These comparisons are done considering trimming, Reynolds number variation and two types of airfoils. Nomenclature AOA Angle of Attack AVL Athena Vortex Lattice AR Aspect Ratio b Aircraft span BWA Box Wing Aircraft CA Conventional Aircraft CD Drag coefficient CD0 Zero-lift drag coefficient CL Lift coefficient CL,ME Lift coefficient for maximum aerodynamics efficiency CL,ME[BWA] Lift coefficient for maximum aerodynamics efficiency of Box Wing Aircraft CL,ME[CA] Lift coefficient for maximum aerodynamics efficiency of Conventional Aircraft DI,BW Induced drag of a box wing DI,CW Induced drag of a conventional wing e Oswald coefficient EBWA Aerodynamics efficiency of Box Wing Aircraft ECA Aerodynamics efficiency of Box Wing Aircraft h Gap. Height between BWA wings h/b Gap to span ratio CL / CD Aerodynamic Efficiency M Mach Number NACA National Advisory Committee for Aeronautics NASA National Aeronautics and Space Administration Re Reynolds Number ReBWA Reynolds Number for Box Wing Aircraft flight ReCA Reynolds Number for Conventional Aircraft flight Vcruise Cruise speed VME Speed of maximum efficiency λ Lambda. Wing taper ratio Copyright 2017 by Fábio Cruz Ribeiro, Adson Agrico de Paula, Dieter Scholz and Roberto Gil Annes da Silva. Published by the EUCASS association with permission. DOI: 10.13009/EUCASS2017-447 Fábio Cruz Ribeiro, Adson Agrico de Paula, Dieter Scholz and Roberto Gil Annes da Silva 1. Introduction The aeronautical industry has been facing significant economic and environmental challenges. To accomplish new market and regulation requirements, the aeronautical engineers are putting efforts in developing new propulsion systems such as more efficient turbines and electric propulsion. Besides, non-conventional aircraft configurations could improve the aerodynamics efficiency substantially as well. The box wing aircraft (BWA) configuration presents an arrangement that increases the aerodynamics efficiency due to its potential lower induced drag and, therefore, lower fuel consumption. However, there are many design aspects that need to be evaluated to propose a BWA configuration as feasible design solution. Torenbeek [1] presents a classification for airplane configurations. One of the categories is the nonplanar lifting system (also known as nonplanar wings) and single body. BWA belongs to this category. It is an airplane which its fuselage is similar to a conventional aircraft (CA) and its lifting system consists of two wings and there is not a horizontal tail. Front wing is aft-swept and rear one is forward-swept. Both wings have their tips connected by vertical fins, see figure 1. Together flying wings, nonplanar wings are being studied as alternative to increase aircraft performance. Figure 1: Box wing aircraft model developed by AERO - Hamburg University of Applied Sciences. [2] Lange et al [3] have studied a BWA for 400 passengers and cruise speed equal to Mach 0.95. They have not achieved the required flutter limit speed due to the low wing stiffness. To overcome this aeroelastic limitation, the penalty of shortening the vertical fins and increasing the aircraft weight have decreased the aircraft performance below an equivalent CA. Gallman [4] and Wolkovitch [5] have researched joined-wing aircrafts (JWA), it is similar to BWA but favors structural aspects once that the length of the vertical fins is zero. Gallman [4] has studied this type of aircraft and has achieved that JWA performance is inferior to CA because additional weight is necessary to comply with buckling requirement of the wing structure. Frediani [6] has studied the relation between the induced drag of box wing divided by the induced drag of a conventional wing and gap to span ratio (h/b). Schiktanz and Scholz [2], [7] investigated a short-medium range BWA design and compared it against a CA. The BWA aerodynamics lead to a better glide ratio, but the BWA is much heavier, due to heavy wings. This leads to more induced drag and more fuel mass compared to the CA. Finally, also the Direct Operating Costs are higher. Longitudinal stability can be achieved also with a BWA, but CG travel is limited. The available fuel volume in the wings does not match requirements. For this reason, additional fuel tanks in the cargo compartment are required. Stability concerns are also reported by Andrews and Perez [8]. They analysed a BWA regional jet. By the BWA literature, it is possible to understand that there is a potential performance gain for box wing configurations when compared to current configurations. However, aerodynamics, flight mechanics and structural designs must be carefully balanced to avoid impediments. This paper studies aerodynamics effects of BWA geometric parameters and compares aerodynamics efficiency between BWA and conventional mid-range size aircraft. 2. Methodology The methodology section is divided in two subsections. The first one explains how the box wing planform is modelled and evaluates effects of geometric variation in the aerodynamics. The second one deals with the comparisons that are carried out between BWA and CA planforms. 2 DOI: 10.13009/EUCASS2017-447 Wing geometric parameter studies of a box wing aircraft configuration for subsonic flight 2.1 Parametric evaluation of box wing aerodynamics This parametric study is carried out using Athena Vortex Lattice (AVL) code and the considered box wing geometry has zero sweep, dihedral and twist angles. A NACA 0012 airfoil is adopted to model the box wing. The airfoil drag polar data is obtained from the literature [9]. The reference wing is kept constant equal to 120 m² and for all cases, the rear and front wing geometries are equal. Figure 2 helps to understand what means stagger and gap. The stagger is the distance in X axis direction between front and rear wings [7]. According Zyskowski [10] “The total induced drag of any multiplane lifting system is unaltered if any of the lifting elements are moved in the direction of the motion provided that the attitude of the elements is adjusted to maintain the same distribution of lift among them”. This excerpt refers to Munk’s theorem. Hence, once that this work will not study wing twist, the stagger effects cannot be evaluated once that twist is necessary to keep the wing loading constant for different values of stagger. However, it may be supposed that its effects in the induced drag would be small. When the stagger is increased, the tip fin wetted area increases as well. Then the aircraft viscous drag increases also. It means that if it is considered only aerodynamics aspects, the stagger should be minimized. Schirra et al [11] presents more details about stagger evaluation of a box wing using AVL. From the literature [1, 6, 7] it is known that the h/b ratio is an important parameter for the BWA aerodynamic characteristics. Hence this parameter is chosen to be variated together with the aspect ratio and taper ratio. Once that the wing area is constant, the aspect ratio is resulted from chosen span values. The adopted range is based on typical mid-range market aircraft. The simulation test matrix is presented in table 1. As can be seen, there are 75 box wing geometries analysed. Figure 2: Key box wing geometric parameters. Table 1: Numerical test matrix for box wing simulation Parameter Values Aspect ratio 8.53 ; 9.63 ; 10.8 Taper ratio 0.2 ; 0.4 ; 0.6 ; 0.8 ; 1.0 Gap over span ratio (h/b) 0.1 ; 0.2 ; 0.3 ; 0.4 ; 0.5 Wing area 120 m² Airfoil for wing and tip fins NACA0012 Once defined the test matrix, the geometries modelled using AVL will be described. First of all, it is necessary to understand that it is not expected to have high fidelity results using vortex lattice methods. Reference [11] has raised limitations of the trailing wake modelling on the induced drag accuracy, for example. The goal of the analysis is to understand the aerodynamics behaviour. The test matrix is simulated with Mach number equal to zero. Then, they do not take account air compressibility effect. To estimate the viscous drag polar, Reynolds number is equal to ten million. According the AVL’s manual [12], the viscous drag is calculated from the two-dimensional airfoil drag polar. To obtain this data, the experimental data available in reference [9] is utilised. One observation about airfoil drag polar calculation consists in the fact that AVL allows the user to insert only one parabolic function for each airfoil. The experimental airfoil drag polar do not obey this function for higher lift coefficients. Then there is accuracy loss in this region. The AVL modelling validation is carried out using two references. Goett and Bullivant [13] present results for wind tunnel tests for a wing (conventional wing) composed by NACA0012 airfoil and aspect ratio equal to six. The experimental procedure is carried out with Reynolds number equal to 3.3 million. These tests are simulated using AVL and the results are compared.